"If Donald is afraid of Megyn Kelly, I would like to invite him on your show to participate in a one on one debate, between me and Donald, mano a mano," Cruz said during a radio interview with Mark Levin on Tuesday night.

"I think every candidate for president owes it to the voters, and in particular owes it to the men and women of Iowa, to go and humble yourself and put yourself before them and answer their hard questions," Cruz said. "Nobody is going to get elected president from a TV studio in Manhattan or New York."

The Trump campaign did not immediately respond to a request for comment regarding Cruz's invitation.

Trump's campaign announced Tuesday that the candidate will "definitely" skip Thursday's GOP debate because he didn't believe he would be treated fairly by Megyn Kelly and the other Fox News moderators.

The Trump campaign's announcement came after several days of heated exchanges between Trump and Fox News, the sponsors of Thursday's GOP debate.

Trump has complained about Kelly's coverage of him since the two clashed at the first GOP debate in August, where Kelly pressed him on controversial remarks he'd made about women.

On Tuesday, he asked his supporters to vote on whether or not he should skip the debate himself.

"Megyn Kelly's really biased against me. She knows that, I know that, everybody knows that. Do you really think she can be fair at a debate?" Trump asked.

Fox News responded to Trump's provocation with some bluster of its own.

"We learned from a secret back channel that the Ayatollah and Putin both intend to treat Donald Trump unfairly when they meet with him if he becomes president -- a nefarious source tells us that Trump has his own secret plan to replace the Cabinet with his Twitter followers to see if he should even go to those meetings," Fox's statement read.

Cruz echoed that sentiment in his own remarks on Levin's show on Tuesday night.

"If Donald is afraid to defend his record, that speaks volumes. If he thinks Megyn Kelly is so scary, what exactly does he think he'd do with Vladimir Putin?" Cruz said. "I promise you Putin is a lot scarier than Megyn Kelly."

Trump responded to Cruz Wednesday on, of course, Twitter: "Even though I beat him in the first six debates, especially the last one, Ted Cruz wants to debate me again. Can we do it in Canada?"

Even though I beat him in the first six debates, especially the last one, Ted Cruz wants to debate me again. Can we do it in Canada?